The only arrival time that matters is differential arrival time, i.e. the time difference between the time a sound reaches each ear.Arrival time is how we localize sound in the world.
Phase coherence is how we tell if it's live or Memorex.
Unfortunately, many tests are performed on the unwashed. Just as some can't tell if a piano is in tune, some can tell you how much it's out, how much it's stretched and the reference A.
If time delay is inaudible, why would manufacturers bother? Spica, Vandersteen, Wilson. Marketing hype? Methinks not.
Today, it's trivial to use DSP to remove displacement delay in multi-amplifier systems. One can model up the analog crossover, make direct driver connections and calculate the driver offset. Next create two presets with and without offset compensation. Switch between them. Let us know.